So I am working on a laboratory experiment which entails taking a heated aluminum sphere and placing it in a wind tunnel. The temperature is then measured as a function of time and from there we are to calculate the heat transfer coefficient (h). All of the data with regards to the sphere is known (temperature, material, geometric) and all of the data with regards to the air is known, or can be calculated, (temperature, Pr, pressure). The trials are repeated for velocities of v=0.4.8,12. From the data the experimental heat transfer coefficient is calculated. The next portion of the lab is to calculate the data with regards to the theoretical heat transfer coefficient. For the values where v=/=0 I found the formula Nu=2+.6(Re)[SUP]1/2[/SUP](Pr)[SUP]1/3 [/SUP]From the Nu number it is pretty much algebra from the definition to determine h Nu=(h*k)/D Now, scanning through my heat transfer textbook, I am unable to find the correct formula with regards to when the velocity of the air is equal to 0. The book discusses the condition and states that the above equation fails when Re->0 but doesn't discuss what to do when that happens. I tried entering 2 as the value of Nu (with little hopes that it would work) but got an theoretical coefficient that was way out of range. Is there another equation that this book is not providing? Or should I be treating this as another scenario? Any and all help would be greatly appreciated ^_^
You said wind tunnel, spheres react differently in horizontal wind tunnels V vertical wind tunnels. I have no idea about the math, But I deign by actually building the items and Spherical dynamic in fluids is something I use a lot, a plane will not flay in a vertical wind tunnel a sphere will do the reverse, it will sit suspended quite easily, basic physics says the experiment vertically is different for in vertical suspension the sphere can be held and not spin, the air flow vertically can be much lower, thus heat dissipation will alter, the rear of the sphere will cool last in either tunnel, contrary to the belief that fluid dynamics surrounds the entire sphere it does not, flowing air hits the face of the sphere becoming the highest pressure point, the even directional path of least resistance is then around the sphere, creating the float in vertical, but at approx 90 - 95 percent of the complete arc of air flow the path becomes straight ahead, thus the only point not being cooled other than via venturi of the passing air. Aluminum is also a product I have worked with a great deal in heating equipment both as a sink and reflector. one experiment had a 100mm block in front of a 600c ceramic heater vertical air extraction was used, the front at 600C 1mm from face had the thermocouple reading attached to the rear read 38 c after several minutes, the aluminum does not sink radiated heat it reflects it even at vast temperatures. unlike a flat block the the sphere will actually dissipate heat in the most uneven manner "because of the wind" if it was simply suspended without the airflow creating a no flow spot and the suspension item could not sink heat,"then" it would dissipate evenly. What you read in books and math is not always accurate, I cant do the math but i can build things patentable level no human has ever seen, my mind understands physics in real terms, not theoretical propositions. ever seen any material dissipate glowing red blow torched heat in ten seconds? I Left school when I was 13 but because of my IQ have been the manager of electrical engineering firms building heating equipment so high tech it was sold "to" the Japanese, there is no math for your equation unless it is simply length of time for the entire sphere to return to its previous total temperature. go to this link https://www.linkedin.com/pub/archie-quinn/18/449/b08 and scroll down to coldrock. it will take you to a video on exactly what you are studying, it will show you that the math you are learning is false, an object can be taken to glowing red hot and without cooling or sink release the heat in seconds, there is no math for it (supposed to be impossible)
Rogue909, when dealing with v <>0 you are dealing with forced convection and your original equation is correct. When dealing with with v=0 then Nusselt's number changes to be a function of Rayleigh and Prandtl. In simple terms Nu = C Ra ^1/4, where C is a function of Pr and Ra can be equated to the diameter of the sphere. See https://www.thermalfluidscentral.or...p/Natural_convection_on_cylinders_and_spheres for more details.
